数学2016researchgate.net
教师需要在教学中纳入数学史吗？
Do Teachers Need to Include the History of Mathematics in Their Teaching? (2003)
入门 · 约 30 分钟读完前置知识：中学数学基础
导读
这篇 2003 年的论文探讨数学教师是否应在教学中融入数学史。讨论呈现两派：支持者认为历史故事和背景能帮助记忆、让数学显得是人类的探索事业；反对者认为对大多数学生数学只是工具，现代表述远比历史路径更清晰易学。
HN 关注点：HN 读者围绕'学数学要不要知道历史'展开争论，焦点在于历史背景是帮助理解还是徒增负担。
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这几条评论里：支持 1 质疑 1 补充 1 亲历 1
支持历史背景和故事能显著帮助理解和记忆
是的，一百个同意。我的数学老师不只教微积分，还讲谁在什么时候做了什么。不用花太多时间，但一点背景帮助很大。所有学科都一样：你需要知道达尔文是 19 世纪的人、热力学大多诞生于 19 世纪末、量子力学是 20 世纪的东西，需要知道当时人们在困惑什么、做了什么实验。像沃森和克里克发现双螺旋这类小故事的意义在于帮助记忆——干巴巴的事实难记，故事好记，人天生如此。
lordnacho查看英文原文
Yes, yes, a hundred times yes. My math teacher taught me not only calculus, but also when and who got up to what. It doesn't have to take a long time, but a bit of context helps a lot. Euler went to Russia and yada yada bridges graphs etc. Same goes for all science disciplines. You need to have a rough idea that Darwin worked in the 19th century, that much of thermo came about in the late 19th century, that quantum is a 20th century thing. You need to know what people were wondering about, and what experiments they came up with. I've been listening to a lot of audio courses lately, and those little nuggets really help to understand things. The point of the little stories such as how Watson and Crick came up with the double helix is to help recall. It's hard to remember dry facts, much easier to remember stories. People are kinda built that way.
质疑数学是工具，对多数人历史是负担，现代方法更高效
恐怕不需要。让普通孩子忍受数学史太残忍了，他们不需要那么多数学。对非数学家来说，数学应被视为工具，就像车床——你不需要知道车床的历史。很少有人需要从最小公理构建数学，博士以下没人该啃怀特海和罗素，现在有定理证明器干这事（1992 年的 Boyer-Moore 证明器一分钟内就能从公理构建构造性数论，我最近把它修好跑在现代机器上并放上了 Github）。更没理由让孩子学牛顿那套微积分记号。
Animats查看英文原文
Probably not. It's interesting to plow through Newman's four volume "The World of Mathematics" as a grad student, but inflicting mathematical history on ordinary school kids is cruel. They don't need that much math. Unless you're a mathematician, math should be viewed as a tool, like a lathe. You don't need to know the history of the lathe, and how Maudslay made it a precision machine tool. (His original lathe is in the Kensington Science Museum. It's one of those historic artifacts which looks very different from its predecessors, and it's successors look a lot like it.) Few people need to know how to build up mathematics from minimal axioms. Nobody should have to struggle through Whitehead and Russell below the PhD level. We have power tools for that now. The original Boyer-Moore theorem prover from 1992 can build up constructive number theory from the axioms in under a minute.[1] I fixed it up recently to run on GNU Common Lisp and put it on Github, so it's runnable on modern machines. There's certainly no excuse for inflicting Newton's notation for calculus on kids. It's not even clear that classical geometry proof approaches are that useful. [1] https://github.com/John-Nagle/nqthm
亲历一线教师亲历：非正式融入数学史效果好
我教高中数学，非正式地融入数学史。比如教圆面积时问学生 π 从哪来——很多学生根本不知道 π 是被人发现的。我画外接正方形、五边形、六边形，问边数一直增加会怎样。学生大部分时间关注数学的实用面，但他们由此明白数学是人类探索的事业，许多部分以美妙而意外的方式拼合在一起。课尾或过渡时间我会放些数学小视频。让数学活起来有很多小办法，分享数学史是其中之一。
japhyr查看英文原文
I teach high school math, and I incorporate math history informally. I don't teach lessons specifically about math history, but I often use it as context for whatever I'm teaching. For example, if I'm showing students how to find the area of a circle, I ask them if they know where pi comes from. Many students have no idea that people had to discover the value of pi, and how it can be used in formulas. To many students, pi and formulas are just things that have been around forever, that they have to learn in school. I draw a square around a circle and ask what the area of a square is. I draw a pentagon and a hexagon, and ask them what will happen if we keep adding sides. Students spend most of their time focusing on the practical aspects of math, but they come away with an understanding that math has been a human endeavor of discovery, and that many of the pieces fit together in beautiful and surprising ways. When we have a little time at the end of class, or during transitions, I pull up little snippets of math to show them. Math videos are great; for example, I love showing students that ∞ + ∞ = ∞. [0] There are lots of little things we can do to make math more alive for students, and sharing some math history is certainly one of them. [0] https://www.youtube.com/watch?v=faQBrAQ87l4
补充视情况而定：历史有时是动机，有时现代讲法远胜历史路径
简短回答：视情况而定。有时历史提供有用的背景和动机，省略它反而让人困惑。但有时现代表述干净得多——即使你想了解历史，先学现代方式、预先知道他们最终走向的真理，一切都会更容易理解。有时历史上的讲法就是很糟。（我上大学学表示论时，教授曾开玩笑地展示'不可约特征标'的原始定义——没人应该那样学表示论！）
Sniffnoy查看英文原文
Short answer: It varies. Sometimes in math the history provides helpful context and motivation, and when people leave it out it makes things confusing. I'm not going to elaborate on this because I assume most people here already agree with this! But sometimes the modern way is so much cleaner and better, so that even if you do want to learn the history, everything will probably be easier to understand if you learn the modern way first and know in advance what truth it is that they were working their way towards. Sometimes the historical way is just awful. (When I took representation theory in college, the professor thought it would be funny to at one point show us the original definition of an irreducible character. Nobody should ever have to learn representation theory in such a way!)
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